An Exponential-Based DGTD Method for Modeling 3-D Plasma-Surrounded Hypersonic Vehicles

Plasma surrounding a hypersonic vehicle can lead to the absorption of incoming radar radiation or the interruption of communication. Therefore, the development of hypersonic vehicle relies on a clear understanding of the strong interaction between the surrounding plasma and the incident electromagnetic wave. However, because of the presence of complex geometrical features and heterogeneous media, these applications are often multiscale. The modeling of such applications in 3-D is extremely challenging for traditional numerical methods. In this work, an efficient discontinuous Galerkin time-domain (DGTD) method for the 3-D modeling of plasma-surrounded hypersonic vehicles is presented. To overcome the grid-induced stiffness problem arising from the modeling of such multiscale applications with dispersive media, and to improve the modeling efficiency, a high-order exponential-based time integration for the time-domain Maxwell's equations discretized by DG schemes with a general flux formulation is proposed. This time integration has excellent stability properties in the locally refined part of the mesh and hence enables the usage of larger time steps compared with the explicit time marching scheme. Additionally, the exponential-based time integration is developed to adapt an anisotropic perfectly matched layer for the modeling of open-domain problems. Finally, numerical experiments are presented to investigate the accuracy and convergence properties and to demonstrate the well-modeling capability of the proposed method.